12 citations · 12 across the 10 of their papers we have counts for
7 papers · 1 filter
Quasi-uniform designs from random candidates: optimal candidate complexity and farthest-point sampling
Takashi Goda, Hengjun Xu
We study randomized constructions of quasi-uniform designs on a compact metric-measure space satisfying two-sided polynomial ball-growth conditions. Given integers , we fir…
Worst-case -approximation of periodic functions using median lattice algorithms
Zexin Pan, Mou Cai, Josef Dick +2
We study the worst-case approximation of multivariate periodic functions from the weighted Korobov space with smoothness in the Lebesgue norm for…
Constructive quasi-uniform sequences over triangles
Hengjun Xu, Takashi Goda
In this paper, we develop constructive algorithms for generating quasi-uniform point sets and sequences over arbitrary two-dimensional triangular domains. Our proposed method, call…
The median trick does not help for fully nested scrambling
Takashi Goda, Kosuke Suzuki
In randomized quasi-Monte Carlo methods for numerical integration, average estimators based on digital nets with fully nested and linear scrambling are known to exhibit the same va…
A simple universal algorithm for high-dimensional integration
Takashi Goda, David Krieg
We present a simple universal algorithm for high-dimensional integration which has the optimal error rate (independent of the dimension) in all weighted Korobov classes both in the…
The Sobol' sequence is not quasi-uniform in dimension 2
Takashi Goda
Are common quasi-Monte Carlo sequences quasi-uniform? While this question remains widely open, in this short note, we prove that the two-dimensional Sobol' sequence is not quasi-un…
A universal median quasi-Monte Carlo integration
Takashi Goda, Kosuke Suzuki, Makoto Matsumoto
We study quasi-Monte Carlo (QMC) integration over the multi-dimensional unit cube in several weighted function spaces with different smoothness classes. We consider approximating t…